A Hydro-Mechanical Constitutive Law for Modelling Sand Production

Solids production is a complex physical process which is controlled by several factors including mechanical failure from in-situ stresses and hydrodynamic erosion from fluid flow. Mathematical and numerical models developed for the prediction of sand production, are usually based on sanding criteria emanating from filtration theories. One of many, is the volumetric sanding criterion which is widely used by the industry and the research community and it is based on a nebulous sand production coefficient λ with dimensions inverse length and with not a specific experimental test to determine it. Additionally, is has been characterized as the erosion strength because experiments show that it is a strong function of plastic shear strains which serve as erosion starting points. In this work, we created a series of finite element models considering the poro-mechanical coupling of the fluid-solid system for simulating hollow cylinder tests in order to to investigate this coefficient. Numerical results are matched on the experimental data of Papamichos et al. (2001) and the mathematical data of Gravanis et al., (2015). By back analysis, the coefficient can be determined and an empirical expression is proposed to describe its behavior as a function of the stress level.